CALib - A Simple Clifford Algebra Library

CALib is a C++ library to manipulate subspace as primitives, based on Clifford Algebra. The code structure is hardly following the 'keep it simple' policy.

Prime Goal

This library is still under construction and will be presented as a final project for the 'GPU Architecture and Programming' discipline, under the watch of the professor D.Sc. Esteban Clua, at UFF.

Available Functionalities

• Manipulate subspaces in a fixed n-dimensional space.
• Automatic cannonical reordering * to mantain an organized basis.
• Outer product *.
• Regressive product *.
• Inner product * with a customizable metric matrix.
• Left contraction * operator.
• Geometric Product *.
• Reverse norm operator.
• Dual operator.

'* CUDA optimized.

Code Organization

The code is organized as follows:

1. Any file sampleX.cu contains the main function and provides an example of how to use the library.
2. The subdirectory calib/* contains all the files used by the library.
3. The subdirectory calib/mode/* contains files that indicate the possible ways of execution ('til now, Host-Only, for CPU version, and Host-Device, for hybrid CPU-GPU version).
4. There are two structs to be used basis.hpp and multivector.hpp.
5. Each one of them has a separated file containing its respectives x_operators.hpp.
6. Available CUDA kernels of the operators are placed in respectives x_operators.cuh files. For any CUDA version operator, there is a called bridge_x method, managing the exchange between the architectures.

Licence

The entire code is released under the GPLv3.

Author

Raphael dos Santos Evangelista and Esteban Walter Gonzalez Clua (Advisor).